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Computational aspects of vector‐like parametrization of three‐dimensional finite rotations
Author(s) -
Ibrahimbegović Adnan,
Frey François,
Kožar Ivica
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620382107
Subject(s) - parametrization (atmospheric modeling) , finite element method , rotation matrix , linearization , matrix representation , representation (politics) , mathematics , rotation (mathematics) , matrix (chemical analysis) , node (physics) , mathematical analysis , geometry , physics , nonlinear system , structural engineering , engineering , materials science , quantum mechanics , politics , political science , law , composite material , group (periodic table) , radiative transfer
Theoretical and computational aspects of vector‐like parametrization of three‐dimensional finite rotations, which uses only three rotation parameters, are examined in detail in this work. The relationship of the proposed parametrization with the intrinsic representation of finite rotations (via an orthogonal matrix) is clearly identified. Careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of Reissner's non‐linear beam theory. Pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2‐node three‐dimensional beam element. A number of numerical simulations in three‐dimensional finite rotation analysis are presented in order to illustrate the proposed approach.